NEW HAMILTONIAN MODEL FOR LONG-RANGE ELECTRONIC SUPEREXCHANGE IN COMPLEX MOLECULAR-STRUCTURES

The electronic superexchange interactions, which enable long-range ele ctron transfer in complex molecular structures, such as proteins, are beyond the capacity of standard electronic structure methods due to th eir size, inhomogeneity, aperiodicity, and sensitivity to the many wea k interactions between the nominally insulating atoms of the interveni ng medium. The inhomogeneous aperiodic lattice theory, presented here, is a novel strategy implemented as a quantum molecular model, designe d to enable the calculation of electronic transfer matrix elements in large macromolecular systems by redesigning the electronic structure p roblem into a two-tiered approach. The procedure is (i) assembly of th e diagonal and off-diagonal elements of the Hamiltonian matrix by comp arison, respectively, with experimental ionization potentials for indi vidual amino acids and with triple-zeta ab initio studies of resonance integrals and then (ii) nonperturbative computation of the macromolec ular electronic coupling from this inhomogeneous aperiodic lattice (IA L) Hamiltonian. The IAL method includes all the occupied orbitals of t he entire protein in a full-matrix calculation with no a priori assump tion about pathways or spatial subregions important in spanning the di stance between the redox sites. The nonperturbative approach and overa ll strategy of subunit-level calibration, distinct from standard semie mpirical atom-level calibration, are first presented. A specific algor ithm for Hamiltonian construction and tests against a series of medium sized molecules then follow. This nonperturbative matrix inversion st rategy is computationally efficient and can treat a system the size of cytochrome c in less than a minute. Most important to the mechanistic study of redox proteins, the absolute results in cm-1 for the compute d charge resonance energies of three ruthenium modified cytochrome c d erivatives compare well with experiment.